In [1]:
import pandas as pd
import numpy as np
from sklearn import svm
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline
from sklearn.svm import svc
In [2]:
def getAccuracy(testSet, predictions):
correct = 0
for x in range(len(testSet)):
if testSet[x]== predictions[x]:
correct += 1
return (correct/float(len(testSet))) * 100.0
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vehicle_df = pd.read_csv("vehicle-1.csv", header = 1)
vehicle_df.head(10)
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In [4]:
vehicle_df.dtypes
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vehicle_df.shape
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vehicle_df.describe().transpose()
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All columns except 'class' are described above. class is the target variable. Except for compactness, max.length_aspect_ratio, max.lenght_rectancgularity and hollows_ratio, all variables have missing values.
In [7]:
sns.countplot(vehicle_df['class'])
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We see that there are around 200 vans and buses and 400+ cars in the class variable.¶
Treatment of the missing values¶
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vehicle_df = vehicle_df.fillna(vehicle_df.median())
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vehicle_df.describe().transpose()
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The missing values have been now replaced by the median of those variable. there are no missing values in the data set now.
Label encoding for Class¶
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from sklearn import preprocessing
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label_encoder = preprocessing.LabelEncoder()
vehicle_df['class']= label_encoder.fit_transform(vehicle_df['class'])
vehicle_df['class'].unique()
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In [12]:
sns.countplot(vehicle_df['class'])
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Van = 0, Car = 1, Bus = 2. This is the conversion of class into numeric values by using lable encoder¶
In [13]:
vehicle_df.info()
Univariate Analysis¶
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sns.boxplot(vehicle_df['compactness'], fliersize=2, orient='v')
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In [15]:
Q1=vehicle_df['compactness'].quantile(q=0.25)
Q3=vehicle_df['compactness'].quantile(q=0.75)
L_outliers=Q1-1.5*(Q3-Q1)
U_outliers=Q3+1.5*(Q3-Q1)
print('Lower outliers in circularity: ', L_outliers)
print('Upper outliers in circularity: ', U_outliers)
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sns.boxplot(vehicle_df['circularity'], fliersize=2, orient='v')
Out[16]:
In [17]:
Q1=vehicle_df['circularity'].quantile(q=0.25)
Q3=vehicle_df['circularity'].quantile(q=0.75)
L_outliers=Q1-1.5*(Q3-Q1)
U_outliers=Q3+1.5*(Q3-Q1)
print('Lower outliers in circularity: ', L_outliers)
print('Upper outliers in circularity: ', U_outliers)
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sns.boxplot(vehicle_df['distance_circularity'], fliersize=2, orient='v')
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In [19]:
Q1=vehicle_df['distance_circularity'].quantile(q=0.25)
Q3=vehicle_df['distance_circularity'].quantile(q=0.75)
L_outliers=Q1-1.5*(Q3-Q1)
U_outliers=Q3+1.5*(Q3-Q1)
print('Lower outliers in distance_circularity: ', L_outliers)
print('Upper outliers in distance_circularity: ', U_outliers)
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sns.boxplot(vehicle_df['radius_ratio'], fliersize=2, orient='v')
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In [21]:
Q1=vehicle_df['radius_ratio'].quantile(q=0.25)
Q3=vehicle_df['radius_ratio'].quantile(q=0.75)
L_outliers=Q1-1.5*(Q3-Q1)
U_outliers=Q3+1.5*(Q3-Q1)
print('Lower outliers in radius_ratio: ', L_outliers)
print('Upper outliers in radius_ratio: ', U_outliers)
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sns.boxplot(vehicle_df['pr.axis_aspect_ratio'], fliersize=2, orient='v')
Out[22]:
In [23]:
Q1=vehicle_df['pr.axis_aspect_ratio'].quantile(q=0.25)
Q3=vehicle_df['pr.axis_aspect_ratio'].quantile(q=0.75)
L_outliers=Q1-1.5*(Q3-Q1)
U_outliers=Q3+1.5*(Q3-Q1)
print('Lower outliers in pr.axis_aspect_ratio: ', L_outliers)
print('Upper outliers in pr.axis_aspect_ratio: ', U_outliers)
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sns.boxplot(vehicle_df['max.length_aspect_ratio'], fliersize=2, orient='v')
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In [25]:
Q1=vehicle_df['max.length_aspect_ratio'].quantile(q=0.25)
Q3=vehicle_df['max.length_aspect_ratio'].quantile(q=0.75)
L_outliers=Q1-1.5*(Q3-Q1)
U_outliers=Q3+1.5*(Q3-Q1)
print('Lower outliers in max.length_aspect_ratio: ', L_outliers)
print('Upper outliers in max.length_aspect_ratio: ', U_outliers)
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sns.boxplot(vehicle_df['scatter_ratio'], fliersize=2, orient='v')
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In [27]:
Q1=vehicle_df['scatter_ratio'].quantile(q=0.25)
Q3=vehicle_df['scatter_ratio'].quantile(q=0.75)
L_outliers=Q1-1.5*(Q3-Q1)
U_outliers=Q3+1.5*(Q3-Q1)
print('Lower outliers in scatter_ratio: ', L_outliers)
print('Upper outliers in scatter_ratio: ', U_outliers)
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sns.boxplot(vehicle_df['elongatedness'], fliersize=2, orient='v')
Out[28]:
In [29]:
Q1=vehicle_df['elongatedness'].quantile(q=0.25)
Q3=vehicle_df['elongatedness'].quantile(q=0.75)
L_outliers=Q1-1.5*(Q3-Q1)
U_outliers=Q3+1.5*(Q3-Q1)
print('Lower outliers in elongatedness: ', L_outliers)
print('Upper outliers in elongatedness: ', U_outliers)
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sns.boxplot(vehicle_df['pr.axis_rectangularity'], fliersize=2, orient='v')
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In [31]:
Q1=vehicle_df['pr.axis_rectangularity'].quantile(q=0.25)
Q3=vehicle_df['pr.axis_rectangularity'].quantile(q=0.75)
L_outliers=Q1-1.5*(Q3-Q1)
U_outliers=Q3+1.5*(Q3-Q1)
print('Lower outliers in pr.axis_rectangularity: ', L_outliers)
print('Upper outliers in pr.axis_rectangularity: ', U_outliers)
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sns.boxplot(vehicle_df['max.length_rectangularity'], fliersize=2, orient='v')
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In [33]:
Q1=vehicle_df['max.length_rectangularity'].quantile(q=0.25)
Q3=vehicle_df['max.length_rectangularity'].quantile(q=0.75)
L_outliers=Q1-1.5*(Q3-Q1)
U_outliers=Q3+1.5*(Q3-Q1)
print('Lower outliers in max.length_rectangularity: ', L_outliers)
print('Upper outliers in max.length_rectangularity: ', U_outliers)
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sns.boxplot(vehicle_df['scaled_variance'], fliersize=2, orient='v')
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In [35]:
Q1=vehicle_df['scaled_variance'].quantile(q=0.25)
Q3=vehicle_df['scaled_variance'].quantile(q=0.75)
L_outliers=Q1-1.5*(Q3-Q1)
U_outliers=Q3+1.5*(Q3-Q1)
print('Lower outliers in scaled_variance: ', L_outliers)
print('Upper outliers in scaled_variance: ', U_outliers)
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sns.boxplot(vehicle_df['scaled_variance.1'], fliersize=2, orient='v')
Out[36]:
In [37]:
Q1=vehicle_df['scaled_variance.1'].quantile(q=0.25)
Q3=vehicle_df['scaled_variance.1'].quantile(q=0.75)
L_outliers=Q1-1.5*(Q3-Q1)
U_outliers=Q3+1.5*(Q3-Q1)
print('Lower outliers in scaled_variance.1: ', L_outliers)
print('Upper outliers in scaled_variance.1: ', U_outliers)
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sns.boxplot(vehicle_df['scaled_radius_of_gyration'], fliersize=2, orient='v')
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In [39]:
Q1=vehicle_df['scaled_radius_of_gyration'].quantile(q=0.25)
Q3=vehicle_df['scaled_radius_of_gyration'].quantile(q=0.75)
L_outliers=Q1-1.5*(Q3-Q1)
U_outliers=Q3+1.5*(Q3-Q1)
print('Lower outliers in scaled_radius_of_gyration: ', L_outliers)
print('Upper outliers in scaled_radius_of_gyration: ', U_outliers)
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sns.boxplot(vehicle_df['scaled_radius_of_gyration.1'], fliersize=2, orient='v')
Out[40]:
In [41]:
Q1=vehicle_df['scaled_radius_of_gyration.1'].quantile(q=0.25)
Q3=vehicle_df['scaled_radius_of_gyration.1'].quantile(q=0.75)
L_outliers=Q1-1.5*(Q3-Q1)
U_outliers=Q3+1.5*(Q3-Q1)
print('Lower outliers in scaled_radius_of_gyration.1: ', L_outliers)
print('Upper outliers in scaled_radius_of_gyration.1: ', U_outliers)
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sns.boxplot(vehicle_df['skewness_about'], fliersize=2, orient='v')
Out[42]:
In [43]:
Q1=vehicle_df['skewness_about'].quantile(q=0.25)
Q3=vehicle_df['skewness_about'].quantile(q=0.75)
L_outliers=Q1-1.5*(Q3-Q1)
U_outliers=Q3+1.5*(Q3-Q1)
print('Lower outliers in skewness_about: ', L_outliers)
print('Upper outliers in skewness_about: ', U_outliers)
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sns.boxplot(vehicle_df['skewness_about.1'], fliersize=2, orient='v')
Out[44]:
In [45]:
Q1=vehicle_df['skewness_about.1'].quantile(q=0.25)
Q3=vehicle_df['skewness_about.1'].quantile(q=0.75)
L_outliers=Q1-1.5*(Q3-Q1)
U_outliers=Q3+1.5*(Q3-Q1)
print('Lower outliers in skewness_about.1: ', L_outliers)
print('Upper outliers in skewness_about.1: ', U_outliers)
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sns.boxplot(vehicle_df['skewness_about.2'], fliersize=2, orient='v')
Out[46]:
In [47]:
Q1=vehicle_df['skewness_about.2'].quantile(q=0.25)
Q3=vehicle_df['skewness_about.2'].quantile(q=0.75)
L_outliers=Q1-1.5*(Q3-Q1)
U_outliers=Q3+1.5*(Q3-Q1)
print('Lower outliers in skewness_about.2: ', L_outliers)
print('Upper outliers in skewness_about.2: ', U_outliers)
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sns.boxplot(vehicle_df['hollows_ratio'], fliersize=2, orient='v')
Out[48]:
In [49]:
Q1=vehicle_df['hollows_ratio'].quantile(q=0.25)
Q3=vehicle_df['hollows_ratio'].quantile(q=0.75)
L_outliers=Q1-1.5*(Q3-Q1)
U_outliers=Q3+1.5*(Q3-Q1)
print('Lower outliers in hollows_ratio: ', L_outliers)
print('Upper outliers in hollows_ratio: ', U_outliers)
Outlier Treatment¶
In [50]:
vehicle_df1 = vehicle_df
for col_name in vehicle_df1.columns[:-1]:
q1 = vehicle_df1[col_name].quantile(0.25)
q3 = vehicle_df1[col_name].quantile(0.75)
iqr = q3 - q1
low = q1-1.5*iqr
high = q3+1.5*iqr
vehicle_df1.loc[(vehicle_df1[col_name] < low) | (vehicle_df1[col_name] > high), col_name] = vehicle_df1[col_name].median()
Outliers have been treated using the median across the entire dataframe.¶
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vehicle_df1.boxplot(figsize=(40,20))
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The missing values and outliers have been treated in the data. The missing values were imputed by applying median in place of missing values. Label encoding was done for the varaible named 'class'. Outlier have been treated as well¶
Bivariate Analysis. Visual Analysis of the data¶
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sns.pairplot(vehicle_df1,hue='class', diag_kind='kde')
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Correlation matrix¶
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cor=vehicle_df1.corr()
cor
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In [54]:
sns.set(font_scale=1.15)
plt.figure(figsize=(20,15))
sns.heatmap(cor, vmax=.8, linewidths=0.01,
square=True,annot=True,cmap="coolwarm",linecolor="black")
plt.title('Correlation between features');
max.length_aspect_ratio, elongatedness, skewness_about, skewness_about1, and hollows_ratio show positive correlation with target variable class.¶
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vehicle_df1.shape
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vehicle_df1.groupby(["class"]).count()
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Class imbalance is checked for. There are more cars in the dataset than vans and buses. The number of cars in double compared to vans and buses and may have an influence on the classification.¶
In [57]:
from sklearn.model_selection import train_test_split
from sklearn import preprocessing
array = vehicle_df1.values
X = array[:,0:18]
Y = array[:,18]
le = preprocessing.LabelEncoder()
le.fit(Y)
test_size = 0.30 # taking 70:30 training and test set
seed = 7 # Random numbmer seeding for reapeatability of the code
X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=test_size, random_state=seed)
type(X_train)
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clf = svm.SVC(gamma= 0.0025, C=3)
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clf.fit(X_train , y_train)
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y_pred = clf.predict(X_test)
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SVM_Accuracy = getAccuracy(y_test , y_pred) # Calling getAccuracy function instead of usinig array comparison to get the %age accuracy
SVM_Accuracy
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Accuracy of SVM Model is 88.98%¶
In [62]:
from sklearn import metrics
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from sklearn.metrics import r2_score
from sklearn.decomposition import PCA
from sklearn.model_selection import KFold
from sklearn.model_selection import cross_val_score
Applying KFold to SVM¶
In [64]:
vehiclekfold_df = vehicle_df1
array = vehiclekfold_df.values
X = array[:,0:18]
y = array[:,18]
X_train, X_test, y_train,y_test = train_test_split(X, y, test_size=0.50, random_state=1)
num_folds = 50
seed = 7
kfold = KFold(n_splits=num_folds, random_state=seed)
results1 = cross_val_score(clf,X, y, cv=kfold)
accuracy=np.mean(abs(results1))
print('Average accuracy: ',accuracy)
print('Standard Deviation: ',results1.std())
Accuracy of SVM model with KFold validation is improved by approx 2% and is 90.80%¶
Applying PCA on the data¶
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covMatrix = np.cov(X,rowvar=False)
print(covMatrix)
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pca = PCA(n_components=6)
pca.fit(X)
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print(pca.explained_variance_)
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print(pca.components_)
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print(pca.explained_variance_ratio_)
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plt.bar(list(range(1,7)),pca.explained_variance_ratio_,alpha=0.5, align='center')
plt.ylabel('Variation explained')
plt.xlabel('eigen Value')
plt.show()
In [71]:
plt.step(list(range(1,7)),np.cumsum(pca.explained_variance_ratio_), where='mid')
plt.ylabel('Cum of variation explained')
plt.xlabel('eigen Value')
plt.show()
With 5 variables we can explain over 99.5% of the variation in the original data! With 3 Variable we are able to explain about 98.9% of the variation¶
In [73]:
pca3 = PCA(n_components=3)
pca3.fit(X)
print(pca3.components_)
print(pca3.explained_variance_ratio_)
Xpca3 = pca3.transform(X)
In [74]:
sns.pairplot(pd.DataFrame(Xpca3))
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Fit SVM Model with PCA¶
In [78]:
SVM_model = SVC()
SVM_model.fit(Xpca3, Y)
SVM_model.score(Xpca3, Y)
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